Digital Filter Designer's Handbook: Featuring C Routines 0079111661, 9780079111661

Table of contents :
Digital Filter Designer's Handbook
Contents
List of Programs
Preface
Ch1 Mathematical Review
1.1 Exponentials & Logarithms
Exponentials
Logarithms
Decibels
1.2 Complex Numbers
Operations on complex numbers in rectangular form
Polar form of complex numbers
Consider three complex numbers:
Multiplication
Division
Powers
Roots
Logarithms of complex numbers
1.3 Trigonometry
Phase shifting of sinusoids
Trigonometric identities
Euler's identities
Series & product expansions
Orthonormality of sine & cosine
1.4 Derivatives
Derivatives of polynomial ratios
1.5 Integration
1.6 Dirac Delta Function
Distributions
Properties of delta distribution
1.7 Mathematical Modeling of Signals
Steady-state signal models
Periodicity
Symmetry
Energy Signals versus Power Signals
1.8 Fourier Series
Trigonometric Forms
Exponential Form
Conditions of Applicability
Properties of Fourier Series
1.9 Fourier Transform
Fourier Transforms of Periodic Signals
Common Fourier Transform Pairs
1.10 Spectral Density
Energy Spectral Density
Power Spectral Density of Periodic Signal
Ch2 Filter Fundamentals
2.1 Systems
Linearity
Time Invariance
Causality
2.2 Characterization of Linear Systems
Impulse Response
Step Response
2.3 Laplace Transform
Background
2.4 Properties of Laplace Transform
Time Shifting
Multiplication
2.5 Transfer Functions
2.6 Heaviside Expansion
Simple Pole Case
2.7 Poles & Zeros
2.8 Magnitude, Phase & Delay Responses
Phase Delay
Group Delay
2.9 Filter Fundamentals
Magnitude Response Features of Lowpass Filters
Scaling of Lowpass Filter Responses
Magnitude Scaling.
Phase Response.
Step Response.
Impulse Response.
Highpass Filters
Bandpass Filters
Wide-Band Bandpass Filters
Narrow-Band Bandpass Filters
Listing 2.1 laguerreMethod( )
Listing 2.2 unwrapPhase( )
Ch3 Butterworth Filters
3.1 Transfer Function
3.2 Frequency Response
3.3 Determination of Minimum Order for Butterworth Filters
3.4 Impulse Response of Butterworth Filters
3.5 Step Response of Butterworth Filters
Listing 3.1 butterworthFreqResponse( )
Listing 3.2 butterworthImpulseResponse()
Ch4 Chebyshev Filters
4.1 Transfer Function
4.2 Frequency Response
4.3 Impulse Response
4.4 Step Response
Listing 4.1 chebyshevFreqResponse( )
Listing 4.2 chebyshevirnpulseResponse(
Ch5 Elliptical Filters
5.1 Parameter Specification
5.2 Normalized-Transfer Function
5.3 Denormalized-Transfer Function
Listing 5.1 cauerOrderEstim( )
Listing 5.2 cauerCoeffe()
Listing 5.3 cauerFreqResponse()
Listing 5.4 cauerRescale()
Ch6 Bessel Filters
6.1 Transfer Function
6.2 Frequency Response
6.3 Group Delay
Listing 6.1 besselCoefficients()
Listing 6.2 besselFreqResponse()
Listing 6.3 besselGroupDelay()
Ch7 FundamentaIs of DigitaI Signal Processing
7.1 Digitization
Ideal Sampling
Instantaneous Sampling
Natural Sampling
Discrete-Time Signals
Notation
7.2 Discrete-Time Fourier Transform
Discrete-Time Fourier Transform
Convergence Conditions
Relationship to Fourier Series
7.3 Discrete-Time Systems
Difference Equations
Discrete Convolution
7.4 Diagramming Discrete-Time Systems
Block Diagrams
Multiplier
Summer
Signal Flow Graphs
Ch8 Discrete Fourier Transform
8.1 Discrete Fourier Transform
Parameter Selection
Periodicity
8.2 Properties of DFT
Linearity
Symmetry
Time Shifting
Frequency Shifting
Even & Odd Symmetry
Real & Imaginary Properties
8.3 Implementing DFT
8.4 Fast Fourier Transforms
8.5 Applying Discrete Fourier Transform
Short Time-Limited Signals
Periodic Signals
Long Aperiodic Signals
Listing 8.1 dft()
Listing 8.2 dft2()
Listing 8.3 fft()
Ch9 z Transform
9.1 Region of Convergence
Finite-Duration Sequences
Infinite-Duration Sequences
Convergence of Unilateral z Transform
9.2 Relationship between Laplace & z Transforms
9.3 System Functions
9.4 Common z-Transform Pairs & Properties
9.5 Inverse z Transform
9.6 Inverse z Transform via Partial Fraction Expansion
Ch10 FIR Filter Fundamentals
10.1 Introduction to FIR Filters
FIR Advantages
FIR Disadvantages
10.2 Evaluating Frequency Response of FIR Filters
10.3 Linear Phase FIR Filters
Listing 10.1 cgdFirResponse()
Listing 10.2 normalizeResponse()
Ch11 Fourier Series Method of FIR Filter Design
11.1 Basis of Fourier Series Method
Properties of Fourler Series Method
11.2 Rectangular Window
Discrete-Time Window
Frequency Windows & Spectral Windows
11.3 Triangular Window
Discrete-Time Triangular Window
11.4 Window Software
11.5 Applying Windows to Fourier Series Filters
11.6 von Hann Window
Discrete-Time von Hann window
11.7 Hamming Window
Discrete-Time Hamming Windows
Computer Generation of Window Coefficients
11.8 Dolph-Chebyshev Window
Listing 11.1 idealLowpass()
Listing 11.2 idealResponse()
Listing 11.3 idealBandpass()
Listing 11.4 idealBandstop()
Listing 11.5 contRectangolarResponse()
Listing 11.6 discRectangularResponse()
Listing 11.7 contTriangularResponse()
Listing 11.8 discTrianguiarResponse()
Listing 11.9 triangularWindow()
Listlng 11.10 makeLagWindow()
Listing 11.11 makeDataWindow()
Listing 11.12 hannWindow()
Listing 11.13 hammingWindow()
Ch12 FIR Filter Design: Frequency Sampling Method
12.1 Introduction
12.2 Odd N versus Even N
Even N
12.3 Design Formulas
12.4 Frequency Sampling Design with Transition-Band Samples
Optimization
12.5 Optimization with Two Transition-Band Samples
Programming Considerations
12.6 Optimization with Three Transition-Band Samples
Listing 12.1 fsDesign()
Listing 12.2 findSbPeak()
Listing 12.3 goldenSearch(0
Listing 12.4 setTrans()
Listing 12.5 goldenSearch2()
Listing 12.6 setTransition()
Listing 12.7 optimize2()
Listing 12.8 dumpRectComps()
Ch13 FIR Filter Design: Remez Exchange Method
13.1 Chebyshev Approximation
Alternation Theorem
13.2 Strategy of Remez Exchange Method
13.4 Selecting Candidate Extremal Frequencies
Testing E(f) for f=0
Testing E(f) within Pass Band & Stop Band
Testing of E(f) at Pass-Band & Stop-Band Edges
Testing of E(f) for f=0.5
Rejecting Superfluous Candidate Frequencies
Deciding When to Stop
13.5 Obtaining Impulse Response
13.6 Using Remez Exchange Method
Deciding on Filter Length
13.7 Extension of Basic Method
Listing 13.1 gridFreq()
Listing 13.2 desLpfResp()
Listing 13.3 weightLp()
Listing 13.4 remezError()
Listing 13.5 computeRemezA()
Listing 13.6 remezSearch()
Listing 13.7 remezStop( )
Listing 13.8 remezStop2()
Listing 13.9 remezFinish()
Listing 13.10 remez()
Ch14 IIR Filters
14.1 Frequency Response of IIR Filters
14.2 IIR Realizations
14.3 Impulse lnvariance
Programming Considerations
14.4 Step lnvariance
Programming Considerations
Listing 14.1 iirResponse( )
Listing 14.2 impulseInvar()
Listing 14.3 stepInvar()
Ch15 IIR Filters via Bilinear Transformation
15.1 Bilinear Transformation
15.2 Factored Form of Bilinear Transformation
15.3 Properties of Bilinear Transformation
Frequency Warping
15.4 Programming Bilinear Transformatlon
Listing 15.1 bilinear()
Ch16 Practical Considerations
16.1 Binary Representation of Numeric Values
Fixed-Point Formats
Floating-Point Formats
16.2 Quantized Coefficients
16.3 Quantization Noise
AppA GlobaI Definitions
AppB Prototypes for C Functions
AppC Functions for Complex Arithmetic
AppD Miscellaneous Support Functions
Bibliography
Index
p250-251 Missing